We report the study, both theoretical and experimental, of the finite-beam Bragg diffraction behavior of an electro-optic (EO) volume grating made ofa periodically poled lithium niobate (PPLN) crystal. When a Gaussian laser beam is used, the experimental observations show that the diffraction characteristics of the PPLN EO Bragg device, including the diffraction mode pattern and diffraction efficiency, are closely related to the interaction beam size and applied voltage, which cannot be modeled properly by a simplified theory using the plane-wave approximation. In this work, we have developed a theoretical model for describing the diffraction behavior of a PPLN EO Bragg device based on the coupled-wave theory with the aid of the plane-wave decomposition method. Specifically, we found that it is the angular distribution (or the dephasing bandwidth) of the plane wave elements decomposed from the incident Gaussian beam and grating strength that determine the Bragg coupling behavior of the device. We also identified some other electro-optically induced effects in the PPLN grating as an important mechanism in affecting the diffraction performance of the present device, especially at high working voltages.